550 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   551 \begin{frame}[c]

   552 \frametitle{Environment}

   553 

   554 Obtaining the ``recorded'' parts of a regular expression: 

   555 

   556 \begin{center}

   557 \begin{tabular}{lcl}

   558   \bl{$env(Empty)$}     & \bl{$\dn$} & \bl{$[]$}\\

   559   \bl{$env(Char(c))$}   & \bl{$\dn$} & \bl{$[]$}\\

   560   \bl{$env(Left(v))$}   & \bl{$\dn$} & \bl{$env(v)$}\\

   561   \bl{$env(Right(v))$}  & \bl{$\dn$} & \bl{$env(v)$}\\

   562   \bl{$env(Seq(v_1,v_2))$}& \bl{$\dn$} & \bl{$env(v_1) \,@\, env(v_2)$}\\

   563   \bl{$env([v_1,\ldots ,v_n])$} & \bl{$\dn$} & 

   564      \bl{$env(v_1) \,@\ldots @\, env(v_n)$}\\

   565   \bl{$env(Rec(x:v))$} & \bl{$\dn$} & \bl{$(x:|v|) :: env(v)$}\\

   566 \end{tabular}

   567 \end{center}

   568 

   569 \end{frame}

   570 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%   

   571 

   572 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   573 \begin{frame}[c]

   574 

   575 \begin{itemize}

   576 \item Regular expression for email addresses

   577 

   578 \begin{center}

   579 \begin{tabular}{l}

   580 (name: \bl{$[a\mbox{-}z0\mbox{-}9\_\!\_\,.-]^+$})\bl{$\cdot @\cdot$}\\ 

   581 \qquad(domain: \bl{$[a\mbox{-}z0\mbox{-}9\,.-]^+$}) \bl{$\cdot .\cdot$}\\ 

   582 \qquad\qquad(top\_level: \bl{$[a\mbox{-}z\,.]^{\{2,6\}}$})

   583 \end{tabular}

   584 \end{center}

   585 

   586 \bl{\[

   587 \texttt{christian.urban@kcl.ac.uk}

   588 \]}

   589 

   590 \item result environment:

   591 

   592 \begin{center}

   593 \begin{tabular}{l}

   594 \bl{$[(name:\texttt{christian.urban}),$}\\ 

   595 \bl{$\phantom{[}(domain:\texttt{kcl}),$}\\ 

   596 \bl{$\phantom{[}(top\_level:\texttt{ac.uk})]$}

   597 \end{tabular}

   598 \end{center}

   599 \end{itemize}

   600 

   601 \end{frame}

   602 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   603 

   604 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

   605 \begin{frame}[c]

   606 \frametitle{Coursework}

   607 

   608 \begin{center}

   609 \begin{tabular}{@ {}l@ {\hspace{2mm}}c@ {\hspace{2mm}}l@ {}}

   610 \bl{$nullable([c_1 c_2 \ldots c_n])$}  & \bl{$\dn$} & $?$\\

   611 \bl{$nullable(r^+)$}                   & \bl{$\dn$} & $?$\\

   612 \bl{$nullable(r^?)$}                   & \bl{$\dn$} & $?$\\

   613 \bl{$nullable(r^{\{n,m\}})$}            & \bl{$\dn$} & $?$\\

   614 \bl{$nullable(\sim{}r)$}               & \bl{$\dn$} & $?$\medskip\\

   615 \bl{$der\, c\, ([c_1 c_2 \ldots c_n])$}  & \bl{$\dn$} & $?$\\

   616 \bl{$der\, c\, (r^+)$}                   & \bl{$\dn$} & $?$\\

   617 \bl{$der\, c\, (r^?)$}                   & \bl{$\dn$} & $?$\\

   618 \bl{$der\, c\, (r^{\{n,m\}})$}            & \bl{$\dn$} & $?$\\

   619 \bl{$der\, c\, (\sim{}r)$}               & \bl{$\dn$} & $?$\\

   620 \end{tabular}

   621 \end{center}

   622 

   623 \end{frame}

   624 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%